Slicing the Oppenheimer-Snyder Collapse: Harmonic versus Maximal Slicing

In continuing our studies of temporal slicings of spacetimes, we consider the collapse from rest of an initially homogeneous dust sphere, known as Oppenheimer-Snyder collapse. It is shown that in the case of harmonic slicing the whole spacetime becomes covered by slices extending to spatial infinity in contrast to maximal slicing. The behavior of the lapse function is discussed, especially for various data on the initial slice, and it is demonstrated that not every choice of the initial lapse leads to meaningful slicings.     

Some remarks on the two-body-problem in geometrodynamics

The interest in the two body problem in geometrodynamics and its present status are discussed. Special consideration is given to time-symmetric initial data. An equation relating the “bare mass energy,” the potential energy and the “vibrational energy” at the initial moment is proposed. The significance of coordinate conditions in dynamical equations is discussed next. Conditions implying maximal slicings of spacetime and harmonic coordinates in those slices are considered in detail, as they seem to be well suited for numerical calculations and for interpretation of the results of such calculations.     

A remark on null infinity

It is shown that to each choice of conformal factor for the conformal metric on future null Infinity (₊) there is associated an equivalence class of slicings of ₊. Each slicing in turn gives rise to a family of null hypersurfaces in the physical space-time.Supported by NSF Grant No. GP-35773X1.     

Large scale silver nanowires network fabricated by MeV hydrogen(H~+) ion beam irradiation

A random two-dimensional large scale nano-network of silver nanowires(Ag-NWs) is fabricated by MeV hydrogen(H~+) ion beam irradiation. Ag-NWs are irradiated under H~+ion beam at different ion fluences at room temperature. The Ag-NW network is fabricated by H~+ion beam-induced welding of Ag-NWs at intersecting positions. H~+ion beam induced welding is confirmed by transmission electron microscopy(TEM) and scanning electron microscopy(SEM). Moreover, the structure of Ag NWs remains stable under H~+ion beam, and networks are optically transparent. Morphology also remains stable under H~+ion beam irradiation. No slicings or cuttings of Ag-NWs are observed under MeV H~+ion beam irradiation.The results exhibit that the formation of Ag-NW network proceeds through three steps: ion beam induced thermal spikes lead to the local heating of Ag-NWs, the formation of simple junctions on small scale, and the formation of a large scale network. This observation is useful for using Ag-NWs based devices in upper space where protons are abandoned in an energy range from MeV to GeV. This high-quality Ag-NW network can also be used as a transparent electrode for optoelectronics devices.     

A new ℋ -space formalism

The equations governing geometrical objects in ? space are written in terms of operators adapted to families of left shear-freeσ ⁰= 0) cross sections of complexified null infinity (C I ⁺). The concept of ?-conformai weight (HCW) is introduced, and a derivative operatorI _a ^′ , which is closely connected with the covariant derivative but which (unlike the covariant derivative) maps objects having well-defined HCW to other such objects, is defined. A function ?, derived from the Gaussian curvature of left shear-free slicings ofC I ⁺ and having a well-defined HCW, is shown to contain all the curvature information for ? space.     

Separable geodesic action slicing in stationary spacetimes

A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent the world lines of freely falling fiducial observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function, although the time coordinate lines still follow Killing trajectories to retain the explicitly stationary nature of the coordinate grid. This explains some of the properties of the original Painlevé-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the Gödel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.     

Lichnerowicz-York equation and conformal deformations on maximal slicings in asymptotically flat space-times

The solvability of the Lichnerowicz-York equation is discussed on each sliceS _t=IR³ of a spacelike, asymptotically Euclidean maximal foliation {S _τ}. Following Cantor, the problem is reduced to a discussion of the properties of a smooth, time-dependent, family of conformal transformations,ø _t, relating the physical metrich _tofS _t to a metric ? _t =ø ⁴h_t, with vanishing scalar curvature. An estimate is provided for infø _t. This allows us to examine the properties of the scale geometry on eachS _twhen strong field regions are probed. It is shown that in such regions ? _t tends to become degenerate exponentially as a suitable average of the scalar curvature of (S _t, h _t ) increases. This is interpreted as representing the approach to a singular regime for (S _t, h _t ). An estimate is also provided for the lapse function-N _t defining {S _t}. This is found to be in agreement with a similar estimate suggested, on heuristic grounds, by Smarr and York. This latter result indicates that asymptotically flat maximal slicings in general (but not always) avoid reaching regions where the above singular regime is approached.     

Smoothness of Time Functions and the Metric Splitting of Globally Hyperbolic Spacetimes

The folk questions in Lorentzian Geometry which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime (M, g) admits a smooth time function whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting if a spacetime M admits a (continuous) time function t then it admits a smooth (time) function with timelike gradient on all M.The second-named author has been partially supported by a MCyT-FEDER Grant, MTM2004-04934-C04-01.To Professor P.E. Ehrlich, wishing him a continued recovery and good health     

Quantum Discord of Non-X State

The level surfaces of quantum discord for a class of two-qubit states are investigated when the Bloch vectors and are perpendicularly oriented. The geometric objects of tetrahedron T and octahedron O are deformed. The level surfaces of constant discord are formed by three interaction "tubes" along three orthogonal directions. They shrink to the center when the Bloch vectors are increased and are expanded and cut off by the state tetrahedron T when the quantum discord is increased. In the phase damping channel, the quantum discord keeps approximately a constant when the time increases.     

Random Walk Quantum Clustering Algorithm Based on Space

In the random quantum walk, which is a quantum simulation of the classical walk, data points interacted when selecting the appropriate walk strategy by taking advantage of quantum-entanglement features; thus, the results obtained when the quantum walk is used are different from those when the classical walk is adopted. A new quantum walk clustering algorithm based on space is proposed by applying the quantum walk to clustering analysis. In this algorithm, data points are viewed as walking participants, and similar data points are clustered using the walk function in the pay-off matrix according to a certain rule. The walk process is simplified by implementing a space-combining rule. The proposed algorithm is validated by a simulation test and is proved superior to existing clustering algorithms, namely, Kmeans, PCA + Kmeans, and LDA-Km. The effects of some of the parameters in the proposed algorithm on its performance are also analyzed and discussed. Specific suggestions are provided.     

Luminance contrast, a new illumination technique in light microscopy: Optical basics, practical evaluations, further developments

Luminance contrast is a new illumination technique in light microscopy recently developed by the author, which leads to extraordinary contrast effects, enhanced focal depth and supramicroscopic resolution when transparent stained or unstained specimens are examined.This method is characterized by a small illuminating light beam running centrically to the specimen, so that the specimen is illuminated very homogenously. Within the objective, the illuminating beam is blocked by a small light stop. When all parts of the illuminating light are totally blocked, the background is completely dark; when small parts of the illuminating light pass the light stop, the background is moderately brightened.The microscopic image is a result of scattered light components, which are bent or reflected by the specimen. When the illuminating light is not completely blocked by the light stop, the transmitted illuminating components interfere with the scattered light components coming from the specimen.Additional three-dimensional effects are achievable when the illuminating light passes the specimen obliquely.The resulting variants of illumination are similar to dark field, negative phase contrast and interference contrast. In all modes of luminance contrast the specimen is illuminated very homogenously so that it appears as a self-luminous, fluorescent body – similar to fluorescence microscopy.Luminance contrast can be carried out when mirror objectives are used or common objectives containing glass lenses are equipped with individually adjusted light stops.Further aspects of technical developments are discussed in full details.     

Transform information: A symmetry breaking measure

A connection between two fundamental concepts of information and symmetry breaking (SB) is established. A concept called transform information (TI) is introduced. The known information measures (Hartley, von Neumann-Shannon-Wiener, Fisher informations, Renyi entropies) can be derived as (or mathematically expressed by) the particular forms of TI for certain transforms of a physical systems (when they are described by the probability measures). As TI is zero when the system is invariant under respective transform, it can be considered, when nonzero, as a quantitative SB measure in the system under study. The classical information measures that are derived from TI also can be perceived as SB measures. This fact is a base for assigning a sense to information. The concept of TI is extended to the cases when systems are described without the use of probability concept.     

Study of characteristics of ultrasound pulse generated by a laser pulse

I.IntroductionThegenerationofacousticpulsebylaserirradiationofametalsurfacewasfirstsuggestcdbyWhitein1963[1l.SincethatdateLaserU1trasoundtechniquchasbeendcvclopedrapidly.Becausethistechniquehasanumberoftechnicalfcatures,suchasnon-contact,highbandwidth,highhme-spacia1resolution,quantitativeteshng,generationoflongitudinal,shcarandRay1cighwaves(simu1taniously),andsoon,ithasbccnwidelyapp1icdtomcasurementsofmatcrialproperties,detectionofdefects,andcalibrationoftransd.ccrsl'-'o].Inordertodcve1opth…     

Interval order and semiorder lattices

When a set of closed intervals of the reals is partially ordered by decreeing that A<B when A lies strictly to the left of B, the resulting structure is called an interval order. Semiorders may be viewed as interval orders that arise from closed intervals having a fixed length. The paper initiates a careful study of interval orders and semiorders that happen also to be lattices. A structure theory is obtained for a class of interval order lattices that includes all such lattices of finite length. Characterizations are given of when these lattices are modular or distributive, as well as when they are semiorders. The theory is of some interest because the completion by cuts of an interval order is necessarily an interval order lattice. Though it is shown that the completion by cuts of a semiorder need not be a semiorder, necessary and sufficient conditions are given for a lattice of finite length to be isomorphic to the completion by cuts of a semiorder.The author wishes to dedicate this paper to the memory of his late colleague Professor Charles H. Randall.     

Phase singularities and coherence vortices in linear optical systems

It is demonstrated for a time-invariant linear optical system that there exists a definite connection between the optical vortices (phase singularities of the field amplitude) which appear when it is illuminated by spatially coherent light and the coherence vortices (phase singularities of the field correlation function) which appear when it is illuminated by partially coherent light. Optical vortices are shown to evolve into coherence vortices when the state of coherence of the field is decreased. Examples of the connection are given. Furthermore, the generic behavior of coherence vortices in linear optical systems is described.     

Design of a solar concentrator combining paraboloidal and hyperbolic mirrors using ray tracing method

A solar concentrator combining primary paraboloidal and secondary hyperboloidal mirrors is numerically designed by using the ray tracing method to obtain higher concentration ratio when the concentrator tracing error exists. It is found that, when the concentrator tracing errors are 0.5° or 1°, the concentration ratios are about 2027 or 1220 without the detector in the radial-direction, and the concentration ratios are about 5447 or 4701 with the detector in the radial-direction. It is shown that such method can increase the concentration solar flux by two folds when the concentrator tracing error exists. Obviously, it is an effective method to reduce the effect of concentrator tracing error even when the angle of concentrator tracing error is considered. In addition, when the angle of concentrator tracing error is small than 1°, a set of mirror shapes is suggested where the primary mirror has a f-number of 0.22 and the secondary mirror has a numerical aperture (NA) of 0.61.     

Complex resonance at periodic excitation of an oscillator

Periodic excitation of an oscillator by an external signal close to an exponential one with a complex frequency at the main part of the period is analyzed. The characteristics of a stabilized excitation regime are determined, as are its features when approaching the complex resonance, when the complex frequency of an external signal at the main part of the period is compared with the complex eigenfrequency of the oscillator. A criterion of closeness to the complex resonance is suggested. Estimations of the allowed level of intensity, when nonlinear distortions of the oscillator response are insignificant, are presented.     

Surface-acoustic-wave-induced space-charge waves in electron-hole systems

Space-charge waves in an electron-hole system are studied, which are excited by a moving grating provided by a surface acoustic wave (SAW). The SAW induces a constant current that may change its sign, when a constant electric field is applied opposite to the wave propagation direction. Current resonances are predicted to appear, when the SAW wavelength and frequency match the ones of the space-charge wave.     

Effects of dipole-dipole interaction on entanglement transfer

A system consisting of two different atoms interacting with a two-mode vacuum, where each atom is resonant only with one cavity mode, is considered. The effects of dipole-dipole （dd） interaction between two atoms on the atom-atom entanglement and mode--mode entanglement are investigated. For a weak dd interaction, when the atoms are initially separable, the entanglement between them can be induced by the dd interaction, and the entanglement transfer between the atoms and the modes occurs efficiently; when the atoms are initially entangled, the entanglement transfer is almost not influenced by the dd interaction. However, for a strong dd interaction, it is difficult to transfer the entanglement from the atoms to the modes, but the atom-atom entanglement can be maintained when the atoms are initially entangled.     

胆甾相液晶温控旋光色散特性的研究

胆甾相液晶的螺距易受温度和电压的影响,螺距变化时,胆甾相液晶的旋光色散特性发生相应的变化。实验证明:温度对胆甾相液晶旋光色散特性的影响与所对应的波长范围有关,在不同的波长范围内,温度对其旋光色散特性的影响规律不同;温度对胆甾相液晶旋光色散特性的影响还与所测试的波长离该温度下选择反射波带的远近有关,离选择反射波带越近,温度对其旋光色散特性的影响越大。实验表明:温度变化时,胆甾相液晶的旋光色散特性的变化是偏振透射谱移动的一个重要原因。